This effect is produced by having a shallow depth of field/focus(DOF). SLR cameras are good at this as the smaller the sensor the larger the depth of field. (your P&S has a very small sensor compared to an SLR camera)

However, the biggest contributor to shallow DOF is the lens aperture so set the max aperture (on P&S the widest possible aperture is usually when zoomed fully out).

The second factor is focal length, by zooming in you get a shallower DOF. In the case of your camera as you zoom in the aperture will get smaller so some experimentation will be needed here

The third step is to have the subject close to the camera and have the background a long way behind the subject.